During the two years Caroline Kennedy worked as a fundraiser and goodwill ambassador for New York City's schools chancellor, Joel Klein, co-workers would frequently drift by her workspace for a glimpse of the department’s most famous $1-a-year employee.

As often as not, they were greeted by an empty chair.

“I’d get it all the time – ‘Why isn’t Caroline at her desk?’” said a person who worked closely with Kennedy, who ran the Department of Education division that oversaw public-private partnerships from 2002 to 2004.

“But that missed the point. She didn’t need to be sitting at a desk,” the person added.

“She kept in touch every single day, by phone, by e-mail or sometimes in person... Or she was out in the field visiting schools.”

A passionate commitment to public education is one of Kennedy’s three main selling points in her bid to win appointment to Hillary Rodham Clinton’s soon-to-be-vacated Senate seat, along with her platinum pedigree and a reputation for above-the-fray rectitude.

Yet because she has taken so few public positions, her education record – or what passes for it – has become just about the only public policy issue on which the 51-year-old political rookie can be judged.

The problem is, she hardly left a vapor trail.

Kennedy, who sent her three children to one of Manhattan’s most exclusive private schools, sat out the epic legal battle to secure billions in state funding for low-income students, and played an ambiguous role during her 22 months as the only city educational bureaucrat routinely harassed by the paparazzi.

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Nevertheless, Klein says Kennedy’s education experience has prepared her “for the big leagues” of the U.S. Senate and describes her as a “highly focused, efficient and hands-on” fundraiser who helped rake in more than $200 million in private-sector contributions for city schools.

“Caroline took over an office that previously oversaw donations to PTAs and alumni associations and recreated it around a model of a public-private partnership,” Klein wrote in an op-ed published Friday.

“The model she created in New York City has led to similar efforts in other school districts across America.”

But several people who worked with Kennedy during her department service take a markedly less grandiose view of her accomplishments.

They say the 51-year-old lawyer and author, while a dedicated advocate for the schools, was less a traditional fundraiser than a highly credible department spokeswoman who used her name to keep big-money donors from fleeing the cash-strapped system.

“She brought us a lot of visibility,” said a person who worked directly with Kennedy, speaking on condition of anonymity. “There was not a lot of fundraising by her personally, but there was a lot of strategizing – ‘Here’s what this organization might do for us,’ – that kind of thing… Her main task was helping to rebuild the credibility of the school system, not directly raising money.”

One business executive familiar with her efforts said that Kennedy provided “star power, not fundraising muscle.”

Kennedy arrived at the Department of Education in 2002, at the behest of Klein and his wife, Nicole Seligman, who ran into her at a party in Martha’s Vineyard, according to press accounts. She was eager to learn about the sprawling system, visiting dozens of schools throughout the city, often riding out by subway, in an effort to boost morale and gauge students’ needs.

Those trips shaped her agenda, associates say: She became especially concerned with the lack of arts funding and began to pressure some donors to direct their contributions to underfunded arts and music programs.

Kennedy’s level of involvement increased the star-wattage of events. She played a central role organizing a Sept. 2003 charitable concert headlined by folk-rocker Dave Matthews and a June 2004 “tag sale” fundraiser with actress Sarah Jessica Parker.

Still, she averaged about only about three hours in the office every day, according to news accounts, and it wasn’t entirely clear what she did the rest of the time. By mid-2004, she was ready to throw herself into a book tour.

When she left, The New York Times wrote: “For months after she started, even some high-level education officials said they were not quite sure what she did. In an interview about eight months into her tenure, she would not say how often she worked at the department headquarters or how many hours she spent on the job, saying only, 'I put in as much time as I can.'"

Kennedy did some direct fundraising, but left the bulk of that work to Klein and several lieutenants, including Leslie Koch, now a city development official, according to a person who worked with her.

In addition, many corporate donors had already been lined up before Kennedy walked through the door, many of them by New York Partnership chief Kathryn Wylde, who personally collected more than $30 million for a leadership academy for principals.

When Klein, speaking to the Times, credited Kennedy with securing $51 million from the Bill and Melinda Gates Foundation for small schools, Wayne Barrett of the Village Voice tracked down officials who claimed the grant was actually set up by Klein deputy Michele Cahill.

Tom Vander Ark, former education director for the Gates Foundation, told Barrett that Kennedy “didn't have anything to do” with obtaining the $51 million.

If opinions differ on Kennedy’s role as an administrator, her positions on several major education issues have proven even harder to nail down.

On Saturday, Kennedy spokesman Stefan Friedman issued her first public statement on education issues, in a brief e-mailed response to several Politico questions.

In it, Kennedy made clear she supported Bloomberg’s effort, spearheaded by Klein, to centralize the city’s education bureaucracy under the direct control of City Hall.

But she stuck to a middle-of-the-road path on other controversial topics, including the ongoing battle over charter schools, publicly funded institutions that are run by non-governmental groups.

Many unions oppose charters, believing they siphon off public school resources and depress teacher salaries by sometimes paying instructors less than their public-school counterparts.

“She supports charter schools, using government money for charters and the right of teachers to organize at charters if they choose,” spokesman Stefan Friedman wrote.

She also took a somewhat noncommittal stance on the Campaign for Fiscal Equity lawsuit, which is expected to funnel billions of new state aid into city schools.

The suit, which was settled several years ago, was unpopular with well-to-do districts in other parts of the state.

“Caroline did not take a public position at the time on CFE, but supports fair funding for New York City schools,” Friedman wrote.

Sarah Morgridge, a Harlem council aide who was part of the lawsuit coalition, praised Kennedy for her work – but questioned why she pursued millions from the companies but didn’t join efforts to pry billions from the state.

“She got some of the icing, but other people baked the cake,” Morgridge joked.